Need to determine turn in Connect Four based on mouse clicks (Mathematica)

I am making a connect four game and I need to figure out which graphic to use (red or black) by how many times the mouse has been clicked. So I need a counter for mouse clicks. That way I can make an If statement: if the counter is odd, use graphic1, if the counter is even use graphic2. This is my code for the graphics then I put them in a list of lists, and make a graphics grid for the game board. Thank you so much!

graphic1 = 
  DynamicModule[{color = White}, 
   EventHandler[
    EventHandler[
     Dynamic[Graphics[{EdgeForm[Thick], color, 
        Disk[{1, 1}, 1]}]], {"MouseDown" :> (color = 
         color /. {White -> Red})}], {"MouseDown" :> (p = 
        MousePosition["Graphics"])}, PassEventsDown -> True]];
graphic2 = 
  DynamicModule[{color = White}, 
   EventHandler[
    EventHandler[
     Dynamic[Graphics[{EdgeForm[Thick], color, 
        Disk[{1, 1}, 1]}]], {"MouseDown" :> (color = 
         color /. {White -> Black})}], {"MouseDown" :> (p = 
        MousePosition["Graphics"])}, PassEventsDown -> True]];